What is 4x^2+6y-32x-y^2+39=0 ?

The solution to 4x^2+6y-32x-y^2+39=0 is Hyperbola with (h,k)=(4,3),a=2,b=4

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4x^2+6y-32x-y^2+39=0

4 x^{2} + 6 y - 32 x - y^{2} + 39 = 0

(h, k) = (4, 3), a = 2, b = 4

Solution steps

4 x^{2} + 6 y - 32 x - y^{2} + 39 = 0

Rewrite

4 x^{2} + 6 y - 32 x - y^{2} + 39 = 0

in the form of a standard hyperbola equation

\frac{( x - 4 ) ^{2}}{2 ^{2}} - \frac{( y - 3 ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, 3), a = 2, b = 4

\frac{x ^{2}}{4} - \frac{( y + 3 ) ^{2}}{9} = 1

x^{2} - y^{2} = 100

\frac{( x + 1 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{16} = 1

\frac{y ^{2}}{36} - \frac{x ^{2}}{4} = 1

25 x^{2} - 4 y^{2} = 100

What is 4x^2+6y-32x-y^2+39=0 ?
The solution to 4x^2+6y-32x-y^2+39=0 is Hyperbola with (h,k)=(4,3),a=2,b=4